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+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements. See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License. You may obtain a copy of the License at
+ *
+ * http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+package org.apache.commons.math.analysis.integration;
+
+import org.apache.commons.math.FunctionEvaluationException;
+import org.apache.commons.math.MathRuntimeException;
+import org.apache.commons.math.MaxIterationsExceededException;
+import org.apache.commons.math.analysis.UnivariateRealFunction;
+import org.apache.commons.math.exception.util.LocalizedFormats;
+import org.apache.commons.math.util.FastMath;
+
+/**
+ * Implements the <a href="http://mathworld.wolfram.com/RombergIntegration.html">
+ * Romberg Algorithm</a> for integration of real univariate functions. For
+ * reference, see <b>Introduction to Numerical Analysis</b>, ISBN 038795452X,
+ * chapter 3.
+ * <p>
+ * Romberg integration employs k successive refinements of the trapezoid
+ * rule to remove error terms less than order O(N^(-2k)). Simpson's rule
+ * is a special case of k = 2.</p>
+ *
+ * @version $Revision: 1070725 $ $Date: 2011-02-15 02:31:12 +0100 (mar. 15 févr. 2011) $
+ * @since 1.2
+ */
+public class RombergIntegrator extends UnivariateRealIntegratorImpl {
+
+ /**
+ * Construct an integrator for the given function.
+ *
+ * @param f function to integrate
+ * @deprecated as of 2.0 the integrand function is passed as an argument
+ * to the {@link #integrate(UnivariateRealFunction, double, double)}method.
+ */
+ @Deprecated
+ public RombergIntegrator(UnivariateRealFunction f) {
+ super(f, 32);
+ }
+
+ /**
+ * Construct an integrator.
+ */
+ public RombergIntegrator() {
+ super(32);
+ }
+
+ /** {@inheritDoc} */
+ @Deprecated
+ public double integrate(final double min, final double max)
+ throws MaxIterationsExceededException, FunctionEvaluationException, IllegalArgumentException {
+ return integrate(f, min, max);
+ }
+
+ /** {@inheritDoc} */
+ public double integrate(final UnivariateRealFunction f, final double min, final double max)
+ throws MaxIterationsExceededException, FunctionEvaluationException, IllegalArgumentException {
+
+ final int m = maximalIterationCount + 1;
+ double previousRow[] = new double[m];
+ double currentRow[] = new double[m];
+
+ clearResult();
+ verifyInterval(min, max);
+ verifyIterationCount();
+
+ TrapezoidIntegrator qtrap = new TrapezoidIntegrator();
+ currentRow[0] = qtrap.stage(f, min, max, 0);
+ double olds = currentRow[0];
+ for (int i = 1; i <= maximalIterationCount; ++i) {
+
+ // switch rows
+ final double[] tmpRow = previousRow;
+ previousRow = currentRow;
+ currentRow = tmpRow;
+
+ currentRow[0] = qtrap.stage(f, min, max, i);
+ for (int j = 1; j <= i; j++) {
+ // Richardson extrapolation coefficient
+ final double r = (1L << (2 * j)) - 1;
+ final double tIJm1 = currentRow[j - 1];
+ currentRow[j] = tIJm1 + (tIJm1 - previousRow[j - 1]) / r;
+ }
+ final double s = currentRow[i];
+ if (i >= minimalIterationCount) {
+ final double delta = FastMath.abs(s - olds);
+ final double rLimit = relativeAccuracy * (FastMath.abs(olds) + FastMath.abs(s)) * 0.5;
+ if ((delta <= rLimit) || (delta <= absoluteAccuracy)) {
+ setResult(s, i);
+ return result;
+ }
+ }
+ olds = s;
+ }
+ throw new MaxIterationsExceededException(maximalIterationCount);
+ }
+
+ /** {@inheritDoc} */
+ @Override
+ protected void verifyIterationCount() throws IllegalArgumentException {
+ super.verifyIterationCount();
+ // at most 32 bisection refinements due to higher order divider
+ if (maximalIterationCount > 32) {
+ throw MathRuntimeException.createIllegalArgumentException(
+ LocalizedFormats.INVALID_ITERATIONS_LIMITS,
+ 0, 32);
+ }
+ }
+}